efficiency in creasing using adaptive

7/28/2019 Efficiency in Creasing Using Adaptive

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ISSN: 2319-8753International Journal of Innovative Research in Science, Engineering and Technology

Vol. 2, Issue 5, May 2013

Bm Friction coefficient [N.m/rad/s]

Kb Induced emf constant [V.s/rad]

kt Torque constant [N.m/A)

T h e industrial u s e application g e n e r a l l y classified into constant-speed and variable- speed drives. Although a

majority of the current variable speed drive applications use dc motors, they are progressively being replaced by ac motor

drives, particularly by the PMSM. This is because the construction of the PMSM incorporates high energy rare-earthalloys, which are responsible for the motors advantageous features such as high torque to current ratio, large power to

weight (or volume) ratio, high efficiency, and high power factor.Drive parameters change due to saturation and/or heating that occur during running. Generally the drive subjected to speed

and load torque disturbance effects that occur during rotating. This makes the motors drive actual response to deviate.

Although the conventional PI controllers have been widely utilized as speed controllers in the PMSM drives, the fixed

gains of these type of controllers is responsible for making the high performance drive systems very sensitive to motor

parameter variations, load torque and speed disturbances under different operating conditions (speed command tracking,

speed command and load torque disturbances, parameter variation), its speed controller has to be capable of self-

tuning, or adapting, its gains automatically online in response to these different operating conditions and increases the

efficiency. These types of controllers are known as adaptive controllers.There are many types of adaptive control techniques that exist today to assist control designers to develop adaptive speed

controllers. Among them are the plant model- based Model Referencing Adaptive Control (MRAC) and Sliding

Mode Control techniques as well as AI-based techniques such as Fuzzy and Neural Control . Recent literature has paidmuch attention to the potential of fuzzy control in machine drive applications. This is because it has the advantages of

providing robust performance for both linear and nonlinear plant functions, and convenience as it does not require

knowledge of the plants mathematical model. However, the qualitative design of the fuzzy logic controller (FLC) is

entirely heuristic, and thus difficult to obtain a systematic design as it is based on ones experiences and expert knowledge

about the process being controlled. Besides that, its input and output scaling gains are determined by trial and error, andhas to be varied to tune the FLC for the desired performance, which altogether makes its design a time- consuming

task. To make the FLC self-adapting towards varying operating conditions, papers such as have proposed that anadditional FLC be included into the control algorithm. This entails more rules and instructions, and thus requiring more

memory and time to execute.

This paper presents an adaptive FLC for the PMSM that is capable of controlling the speed of the motor to track any

arbitrary selected reference position and speed despite motor parameter variations, load torque and speed disturbances. The

design of the proposed controller incorporates a function known as FTAG that automatically adjusts the output gain of the

FLC according to the load applied onto the motor. The paper is organized as follows: the motor dynamics of the PMSM isreviewed; in the concept of the ANFIS technique is briefly explained; in Section 4, the development process of FTAG FIS

is presented; a speed control performance comparison is made between developed FTAG FIS and the conventionalPI Controller; and finally, in Section 6, concluding remarks end the paper.

II. DRIVE OF THE PMSM

Upon employing the vector control scheme, the dynamic model of the PMSM can be represented mathematically by the

following equations in the d-q axis synchronously rotating rotor reference frame (under sinusoidal stator excitation) where

vq and vd are the d, q axis voltages, Ld and Lq are the d, q axis inductances, id and iq are the d, q axis stator

currents, respectively; R is the stator resistance per phase, f is the rotor flux linkage, m is the mechanical angular

rotor speed, P is the number of pole pairs of the motor, Te is the developed electromagnetic torque, TL is the load

torque applied to the motor, Jm is the moment of inertia and Bm is the motor friction coefficient.

III. ANFISThe Adaptive Neuro- Fuzzy System, or ANFIS, was proposed by Roger Jang from the Tsing Hua University, Taiwan,

back in 1993. According to Jang, the ANFIS is a neural network that is functionally equal to a Sugeno type inference

model.

IV. FUZZY LOGIC

The general methodology of reasoning in FL is by the IFTHEN rules. From Fig. 1 below, a fuzzy inference system (or

FIS) basically consists of a formulation of the mapping from a given input set to an output set using fuzzy logic [1]. This

mapping process consists of five main steps. The first step in the mapping process is to fuzzify the crisp input variables, X

and Y, which is done by mapping them to the membership functions (MFs) of the fuzzy variables. The second step in the


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mapping process is the application of the fuzzy operator (AND, OR, NOT) in the IF (antecedent) part of the rule,followed by the implication from the antecedent to the consequent (THEN part of the rule) [1]. As the ANFIS is based on

the Sugeno type inference model, only the Sugeno implication method will be explained here. The Sugeno method can be

defined in two ways: the zero-order and the first-order method. In the Sugeno zero-order method, the fuzzy output MFs are

only constants; as in the fuzzy output, Zn = constant, Kn, as shown in Fig. 1. In the Sugeno first-order method, the fuzzy

output MFs have linear relations with the inputs; as in the fuzzy output, Zn, is mathematically expressed as,

(X)

1

(Y)

NS0.8

ZE

0.6

(Z)

1

Rule- 1DOF1 = 0.6

-6 0 6

(X)

-6 0 6

(Y)

-6 0K1

6

(Z)

1

Rule- 2

ZE1

ZE1

0.6

0

DOF2 = 0

-6 0 6 -6 0 6 -6 0 6K2

(X)

1

(Y)

NS PS0.8

11.0

(Z)

1

Rule- 3DOF3 = 0.8

-6 0 6

X = -5

-6 0 6

Y = 2.5

-6K3

0Z

6

Fig. 1. A two-input, three-rule fuzzy system using Sugeno (zero- order) method.

Where all the As are constants. The fourth step in the mapping process is the aggregation of the consequentsacross all the rules [1], where the total fuzzy output, Zf, is the union (OR) of all the individual fuzzy outputs,

Zn. The final step in the mapping process is the defuzzification of the total fuzzy output, Zf, to Z0, where Z0 is

the crisp output value of the FIS as a result of the crisp input values X and Y. The defuzzification formula for aSugeno FIS type is, where n denotes the rule number; N, the total number of rules in the rule base; andDOF, the Degree of Fulfillment.

V. ARTIFICIAL NEURAL NETWORK (ANN)

An ANN is a model that is made to simulate the biological nervous system of the human brain. It is trained, not

programmed such as the rule- based FLC, to learn by example from the sets of input-output training data fed

into it. The ANN results from the interconnection of artificial neurons via weights that act like gains. A non-linear activation function contributes to the non-linear transfer characteristics of a neuron, which permits non-

linear input-output mapping in a neural network (NN). The learning (or training) process of the network has

been illustrated simply in Fig. 2 where the training algorithm adjusts the values of the weights until the networkoutput matches the target.


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Fig. 2. Simplified schematic of the ANN training process.

VI. ADAPTIVE NEURO- FUZZY INFERENCE SYSTEM (ANFIS)

Though the MFs of the FIS have to be manually adjusted by trial-and-error, the FIS acts like a white box,

meaning that the control designers are able to understand how the controller reached its solution. On the otherhand, the NN can learn, but acts as a black box as to how it had reached to a particular solution. By employingthe NN approach to develop the parameters of the FIS, the FIS is given the ability to learn from a given setof training data, just like an ANN. At the same, the solutions mapped out onto the FIS can be explained inlinguistic terms. This learning process of the FIS is illustrated in Fig. 3 where the parameters of the MFs andSugeno output functions, f1 and f2, are adjusted by the Back propagation (BP) algorithm (one of many training

algorithms) until the FIS output matches the target. A more detailed explanation of ANFIS can be found.

VII. IMPROVEMENT OF FTAG FIS

This section summarizes the methodology that was adopted to develop the adaptive FTAG FIS speed controlalgorithm for the PMSM, which can be subdivided into 4 phases.

VIII. ALGORITHM DEVELOPMENT: REFERENCE PMSM MODEL

An extensive experimentation was initially carried out to determine the best method that generates the most

appropriate training data from which the FIS can learn from, the best initial FIS architecture parameters that has

the best learning ability, and the most appropriate training method to train the FIS. The adaptive speed controller

that was developed at this stage was based on the reference PMSM model that was derived in (4) and (5).

Theoretically, from equations (1)- (5), the control principle between the dynamic and reference PMSM model is

the same, thus, the developed controller for the reference model should be a good approximate to that required

by its dynamic counterpart.

The input-output training data that was used to train the FIS was generated from the PMSM reference model.The speed error, e (rad/s), and the rate of change in speed error, ce (rad/s), was collected to be the input trainingdata whilst the command torque current, Iq* (A), was the output training data. Many training sessions was

carried out using the MATLAB ANFIS Editor GUI to determine the type, number and range of training data thatwould facilitate the most efficient training of the FIS to be an adaptive speed controller. For the type of data, it

was found that training the FIS with data that were generated at both the No-Load (NL) and Full-Load (FL)condition of the motor is sufficient for the FIS to generalize for all the other load conditions in between. Thenumber of training data used should also be in proportion to the number of FIS parameters being estimated bytheANFIS.


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IX. FIRST-MID PHASE OF ALGORITHM DEVELOPMENT:DYNAMIC PMSM MODEL AT

NL CONDITION

In the previous section, it was mentioned that the adaptive speed control algorithm for the dynamic PMSM

model could be developed using its reference model. However, this was not the case. This was probably

due to the complicated dynamics of the actual PMSM that was not properly represented by the nature of

the training data generated from the reference PMSM model, and thus, was not properly mapped by the FISupon training it. Therefore it is required to generate the training data directly from the dynamic PMSMmodel to train the FIS. However, it was very difficult to generate good training data from the random

1 rad/s step speed commands that was applied on to the dynamic PMSM model as was done previously

with its reference model (i.e. random 1 rpm step speed changes), even at NL condition. This problem

was resolved by generating 10 sets of training data from10 step speed changes; 1 rad/s,10 rad/s, 100

rad/s, 314 rad/s, and 628 rad/s (motors rated speed). This was toensure that the entire range of the

motor speed was covered. This led to thedevelopment of an adaptive FLC for the NL condition of the

dynamic

PMSM model.

Fig. 5. The initial parameters of the input trapezoidal MFs that were used to define the (a) speed error,

e, and (b) change in speed error, ce.

The architecture that was described previously was used, except that the bell MFs were replaced withtrapezoidal MFs that were uniformly distributed across the input range, as shown in Fig. 5. Here is an

example of a rule taken from the table: IF wm is very much slower than wm*, i.e. e is wm


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Fig. 6. Reversing transient of (a) rated and (b) 1% rated reference speed settings

(at NL condition). Unity output gain.

Upon training the FIS at NL condition, a FLC that is not only able to adapt to variations in the motor

parameters, but also respond effectively to small and large reverse transients was successfully developed.This is referred to as FIS dyNLtra, and its superiority at the motors NL condition has been illustrated in Fig.

6. However, the developed algorithm was unable to track the command speed at situations when there were

load torque disturbances of any kind as it was trained only with NL data.

X. SECOND-MID PHASE OF ALGORITHM DEVELOPMENT: DYNAMIC PMSM

MODEL AT FL CONDITION

In this phase, a FIS was trained with training data that was generated from the dynamic PMSM

model at FL condition. In generating the training data from the dynamic PMSM model at FL condition, it was

found that the methodology that was used previously at the NL condition could not be employed. After

trying out several methods, it was finally decided to generate the data sets from only the positive speedoperating mode of the PMSM. This was based on the assumption that the FIS would be able to learn from

its ANFIS training to adapt to the negative speed reference settings. The procedure from here on is the same

as before. The 5- 3- 15 FIS architecture as before was used as the initial FIS architecture.

Upon training the FIS at FL condition, a FLC that has good speed tracking performance at both low and highspeeds, even with variations in the motor inertia, J, inductance, L, and resistance, R, was developed. It has

also proven itself to be able to respond effectively to reverse transients during high and 0low speeds as

shown in Fig.7. This FIS is referred to as dyFLtra. However, as before, the developed algorithm was

unable to adapt itself to any other load torque applications aside from FL.


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Fig. 7. Reversing transient of (a) rated and (b) 1% rated reference speed settings

(at FL condition), with a constant output gain of 0.645.

XI. FINAL PHASE OF ALGORITHM DEVELOPMENT: FTAG FIS

The final phase of the algorithm development involves training the FIS with both the NL and FL training data

that were generated previously to develop a fuzzy speed controller that will be adaptive towards allpossible operating conditions of the PMSM, including during load torque disturbances. This resulted in the

self-adapting, speed controller, FTAG FIS algorithm. The NL and FL data sets that were generated previously

were combined together into a data pool. The data sets were stacked on top of the other, alternating

between the NL and FL data sets; in a manner such that the speeds were grouped in a descending

order to facilitate the training process of the FIS.For the initial FIS architecture, the 5- 3- 15 FIS architecture

was used as before. The FIS that was trained at NL and FL condition is referred to by the name nftrap. Upon

simulating the FISnftrap, it was observed that the amount of SSE increases as

the amount of load torque applied decreases. Based on observation and tuning, a list of output gains, Gob,

was generated for the different load torque applications.

To convert the non-linear characteristic of the load torque, TL, into a linear one, the output gains, Goa, for eachload torque value were approximated such that the gains were equally displaced from one another by 0.173for every load change of 0.1 Nm. Thus, the following linear relationship between T L, and FLC output gain,Goa, could be derived:

Approx.OutputGain = f(Load Torque) (10)

Goa=m

TL

(11)

Where the linear slope, m, between TL and Goa is a constant 0.173. However, for accuracy, the value of m

was represented as a fraction of 1.04/0.6. The load torque, TL, can be estimated from equation (4). The

complete configuration of the developed adaptive controller is illustrated in Fig. 8, which is called theFunction Torque Adapted Gains Fuzzy Inference System (FTAG FIS) because the output gain of FLC nftrapis adjusted accordingly to the amount of TL applied onto the PMSM. The FTAG FIS has been tested

for loads as low as 0.05 Nm (to approx. the motors NL condition), and had exhibited good speed trackingperformance, even at unity input gains.


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Fig. 8. The configuration of the FTAG FIS speed control algorithm.

XII. DIFFERENCE BETWEEN SIMULATED SPEED RESPONSES OF DEVELOPED

FTAG FIS AND PI CONTROLLER0

In this section, a thorough comparison between the developed adaptive speed control algorithm, FTAG FIS,

the FIS nftrap, and the conventional PI controller is made to observe the robustness of the developed FTAG

FIS. The following set of benchmark tests was used as a guide to evaluate the controllers performance:

Large step speed command from standstill, under rated inertia condition andwith increases inertia;

Small reference speed change, with rated and with increased inertia;

Step load torque application;

Reversing transient.

The above benchmark tests were proposed by Z. Ibrahim and E.Levi in [12]. Unlike many papers that onlycarry out their comparisons at a single transient or single operating point, these benchmark tests are

performed at both high and low reference speed settings; 628 rad/s and 10 rad/s, respectively, to justify the

validity of the evaluation and comparison of the speed controllers.The FIS controller nftrap was simulated

with a constant output gain of 0.645 to illustrate the effect of not employing an adaptable gain such as that

used in the FTAG FIS algorithm. As for the PI controller, the initial Kp and Ki gains that were used were the

same gains that were used to generate the training data to train the FIS dyNLtra and nftrap, both of which

were used to develop the FTAG FIS algorithm.

Fig. 9. Response to (a) 628 rad/s and (b) 10 rad/s step speed command from standstill (rated inertia J),

at NL condition.


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From the simulated results in Fig. 9 to Fig. 12, one may conclude that the PI controller has better speed

control performance than the developed FTAG FIS algorithm; with faster speed tracking response at both

low and high speeds, even during motor parameter variations (where motor inertia J is twice the rated

value) and sudden speed changes (where a step 10% speed reference reduction from the command

speed). However, it should be highlighted to the reader that the PI controller gains that were used atrated and low speeds had to be manually tuned each time. The reason the three controllers speed

performance was tested at rated and 10 rad/s reference speed setting is because the optimum PI gains for

these speeds were already known. At any other (lower) reference speeds, the optimum PI gains would have

to be found by trial and error. Besides that, it is also desired to illustrate the competitive advantage that

FTAG FIS has over the PI controller at operating conditions from which the FIS training data were

generated. Though the PI controller has the fastest transient time among the three, the developed FTAG FIS

is only about 1 to 5ms slower than the PI controller, with negligible SSE as well.

Fig. 10. Response to step 10% speed reference reduction from (a) 628 rad/s and

(b) 10 rad/s (rated inertia J), at NL Condition.

Fig. 11. Response to (a) 628 rad/s and (b) 10 rad/s step speed command

The superiority of the developed FTAG FIS algorithm over the conventional PI controller and even the FISnftrap can be observed in its response to sudden load torque disturbances and reversing transients in Fig.13 and 14, respectively. From Fig.13, it is clear to see that FTAG FIS was able to adapt itself efficiently froma NL to a FL condition, without requiring any user intervention. Though the PI controller can be adjusted to

provide a similar or even possibly better load rejection transient than FTAG FIS, the point that is desiredto be made here is that FTAG FIS will automatically adjust itself to any operating condition that it is in to


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ensure that the motor will track the reference speed setting in a short recovery time with negligible SSE. TheFTAG FIS also yields a rapid speed reversal with no overshoots. On the other hand, the PI controller ischaracterized with over and undershoots that are significantly large and harmful to the motor at low speeds.In short, the developed FTAG FIS offers superior speed tracking performance, speed recovery from suddenload torque and speed changes, and speed reversals at both low and high speeds, even during variations in the

motor parameters.

Fig. 12.Response to step 10% speed reference reduction from (a) 628 rad/s and

(b) 10 rad/s (increased inertia J), at NL Condition.

XIII. CONCLUSION

This research paper has under development FTAG FIS, an adaptive speed controller for the PMSM using

the Adaptive Neuro-Fuzzy Inference System. After The developed control algorithm has been verifiedthrough simulations to be not only more superior to the conventional PI controllers, especially during load

torque disturbances, but also to be robust during speed changes, speed disturbances, as well as variations in

the motor parameters it also increase the efficiency. The control algorithm design methodology that has been

presented in this paper shows its effectiveness in eliminating the need for the control designer to adjust the

input and output gains of the fuzzy controller manually by trial and error. On top of that, it has disguised the

non-linear characteristic of the load torque into one that is linearly related to the output gain of the

developed fuzzy controller. The FTAG FIS algorithm guarantees the closed loop performance of the PMSM

even when the motor is subjected to significant and unpredictable motor parameter variations and load torquedisturbances at both low and high speeds. An outstanding advantage of the FTAG FIS algorithm for the

PMSM is that it uses only15 rules in its rule base, which is less than half the number of rules that is being

used in many other fuzzy controllers that have been proposed in the literature. With fewer rules, the FTAG

FIS is not only more easily implemented, but will have shorter execution time. Suggestions for further work

include a real time implementation of the algorithm onto the motor to verify whether there is a closeagreement between the theoretical and experimental results and modifying the current FTAG FIS algorithm

to incorporate one, and

not two, FIS.


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Fig. 13. Response to step load torque applications at (a) 628 rad/s and (b) 10 rad/s reference speed

settings, from NL to FL Condition.

Fig. 14. Reversing transient (a) 628 rad/s and (b) 10 rad/s reference speed settings, at Rated

Conditions.


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References

1. Rahman, M.A., Vilathgamuwa, D.M., Uddin, M. N. and Tseng, K.J. (2003).Nonlinear Control of Interior Permanent- Magnet Synchronous Motor. IEEE Transactions on Industry Applications. 39

(2), 408-416.2 .Rahman, M . A ., U d d i n , M . N . and A b i d o , M . A . (2004). D e v e l o p m e n t a n d Implementation of a Hybrid

Intelligent Controller for Interior Permanent- Magnet Synchronous Motor Drives. IEEE Transactions on Industry

Applications. 40(1),68-76.

3. Heber, B., Xu, L. and Tang, Y. (1997). Fuzzy Logic Enhanced Speed Control of an Indirect Field- Oriented InductionMachine Drive. IEEE Transactions on Power Electronics. 12(5), 772-778.4. Zhen, L. and Xu, L. (2000). Fuzzy Learning Enhanced Speed Control of an Indirect Field- Oriented Induction

Machine Drive.IEEE Transactions on Control Systems Technology. 8(5), 270-278.

5. Negnevitsky, M. (2002). Artificial Intelligence: A Guide to Intelligent Systems,1st

ed., Addison Wesley, Pearson

Education Limited.

6. Math Works Inc. (2004).Neural Network Toolbox For Use with Matlab

UsersGuide Version 4.7. Zilouchian, A. and Jamshidi, M. (2001). Intelligent Control Systems Using SoftComputing Methodologies, BocaRaton, FL: CRC Press.

8. Lin, C.T. and George, C.S. (1996).NEURAL FUZZY SYSTEMS: A Neuro- FuzzySynergism to Intelligent Systems, Upper

Saddle River, NJ: Prentice- Hall PTR. Math Works Inc. (1998). Fuzzy Logic Toolbox For Use with Matlab

UsersGuide Version 2.9. Ibrahim, Z. and Levi, E. (2000). A Comparative Analysis of Fuzzy Logic SpeedControl in High Performance ACDrives Using Experimental Approach. IEEE, 1217-1224.

10. Kouzi, K., Mokrani, L. and Nait- Said M.S. (2003) A Fuzzy Logic Controller withFuzzyAdapted Gains Based onIndirect Vector Control for Induction Motor Drive.Journal of Electrical Engineering, 3, 43-49.

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